-5x-2/3x=17

Solution for -5x-2/3x=17 equation:

-5x-2/3x=17

We move all terms to the left:

-5x-2/3x-(17)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


-5x*3x-17*3x-2=0

Wy multiply elements

-15x^2-51x-2=0

a = -15; b = -51; c = -2;
Δ = b2-4ac
Δ = -512-4·(-15)·(-2)
Δ = 2481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2481}}{2*-15}=\frac{51-\sqrt{2481}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2481}}{2*-15}=\frac{51+\sqrt{2481}}{-30}
$